Lyric discussion by The Kitten 

Cover art for Eisbär lyrics by Dresden Dolls, The

This song has no meaning at all, it comes from a certain eighties "music era" (if you will), called "Neue deutsche Welle" (new german wave, "wave" just meaning "a wave", not referring to the style "new wave"). The point is, that during that time synthesizers became available, so people thought it would be much easier to form bands and write music. Thousands of german bands started to spring from the ground, writing simple songs with naive, meaningless lyrics (remember "DaDaDa"). Many americans wondered if there were any hidden meanings behind those obviously dunb texts, but, unlike with certain songs of other periods, there simply aren't any. All that mattered was to come up with some something that rhymed. Note: there isn't even a german word "polar", it is either "Pol" (pole) or "Nordpolarmeer" (arktic ocean). Otherwise, the word is only used as an adjective, meaning "connected to the Pole regions" and never appears alone (Polar-Express, Polar-Station etc.) Neither would fit in length or rhyme with "klar", so they just made something up.